Question: Simplify the following expression: $ z = \dfrac{2y + 2}{-10} - \dfrac{-9}{4} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{2y + 2}{-10} \times \dfrac{4}{4} = \dfrac{8y + 8}{-40} $ Multiply the second expression by $\dfrac{-10}{-10}$ $ \dfrac{-9}{4} \times \dfrac{-10}{-10} = \dfrac{90}{-40} $ Therefore $ z = \dfrac{8y + 8}{-40} - \dfrac{90}{-40} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{8y + 8 - 90 }{-40} $ Distribute the negative sign: $z = \dfrac{8y + 8 - 90}{-40}$ $z = \dfrac{8y - 82}{-40}$ Simplify the expression by dividing the numerator and denominator by -2: $z = \dfrac{-4y + 41}{20}$